What question did this study set out to answer?

To analyze asymptotic convergence toward phase-homogeneous equilibrium states and establish quantitative error estimates for the diffusion limit within the inertial Kuramoto–Sakaguchi model.

September 17, 2026SIAM Journal on Mathematical AnalysisOpen Access

Trend to Equilibrium and Diffusion Limit for the Inertial Kuramoto–Sakaguchi Equation

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Authors

FFFrancis Filbet MKMyeongju Kang

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Overview

Mathematical analysis demonstrates convergence to equilibrium and establishes explicit error estimates for the diffusion limit in interacting oscillatory systems, indicating enhanced stability bounds.

Key Points

To analyze asymptotic convergence toward phase-homogeneous equilibrium states and establish quantitative error estimates for the diffusion limit within the inertial Kuramoto–Sakaguchi model.
Analyzed the inertial Kuramoto–Sakaguchi equation describing populations of weakly coupled interacting oscillators.
Applied weighted Lebesgue norm estimates to assess long-term convergence under small coupling regimes.
Derived quantitative error estimates for the zero-mass diffusion limit by imposing mild regularity conditions on identical oscillator ensembles.
Proved asymptotic convergence toward phase-homogeneous stationary states across a broader function space than previous Sobolev-based frameworks.
Obtained explicit, mass-dependent error estimates for the diffusion limit in identical oscillator systems, resolving previous limitations of non-constructive compactness methods.

Cite This Study

Filbet et al. (2026) studied this question.

synapsesocial.com/papers/6aabb5fd5f706d05830e4667 https://doi.org/10.1137/23m1612597

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September 17, 2026SIAM Journal on Mathematical AnalysisOpen Access

Trend to Equilibrium and Diffusion Limit for the Inertial Kuramoto–Sakaguchi Equation

View Full Paper

Ask AI

Bookmark

Authors

FFFrancis Filbet MKMyeongju Kang

Discussion

Member takes

Overview

Key Points

To analyze asymptotic convergence toward phase-homogeneous equilibrium states and establish quantitative error estimates for the diffusion limit within the inertial Kuramoto–Sakaguchi model.
Analyzed the inertial Kuramoto–Sakaguchi equation describing populations of weakly coupled interacting oscillators.
Applied weighted Lebesgue norm estimates to assess long-term convergence under small coupling regimes.
Derived quantitative error estimates for the zero-mass diffusion limit by imposing mild regularity conditions on identical oscillator ensembles.
Proved asymptotic convergence toward phase-homogeneous stationary states across a broader function space than previous Sobolev-based frameworks.
Obtained explicit, mass-dependent error estimates for the diffusion limit in identical oscillator systems, resolving previous limitations of non-constructive compactness methods.

Cite This Study

Filbet et al. (2026) studied this question.

synapsesocial.com/papers/6aabb5fd5f706d05830e4667 https://doi.org/10.1137/23m1612597

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